Finite Group Databasebeta

← #11069167

Subgroups — #11069167

Order 768.

2484 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5697C212yesmaximal, complemented
2C3×#2552C211yesmaximal, characteristic, complemented
3#83030C212yesmaximal, complemented
4#77967C214yesmaximal, complemented
5#77853C214yesmaximal, complemented
6#76249C212yesmaximal, complemented
7#76215C212yesmaximal, complemented
8#76211C212yesmaximal, complemented
9#76004C212yesmaximal, complemented
10#74375C211yesmaximal, characteristic, complemented
11#74368C212yesmaximal, complemented
12#74360C211yesmaximal, characteristic, complemented
13#74328C212yesmaximal, complemented
14#73799C211yesmaximal, characteristic, complemented
15C4×#895C211yesmaximal, characteristic, complemented
16#73753C211yesmaximal, characteristic, complemented
17#73653C211yesmaximal, characteristic, complemented
18#39352—31nomaximal, Sylow
19C2×C3×#125C2212yes—
20#5697—216no—
21C2×#895C2214yes—
22C2×#895C2212yes—
23C2×#895C2214yes—
24C2×#895C2212yes—
25C2×#895C2212yes—
26C2×#895C2212yes—
27C2×#895C2212yes—
28C2×#895C2211yescharacteristic
29C2×#894C2214yes—
30C2×#894C2214yes—
31C2×#894C2214yes—
32C2×#893C2212yes—
33C2×#893C2212yes—
34C2×D3×C4⋊C4C2212yes—
35C2×#874C2212yes—
36C2×#874C2211yescharacteristic
37C2×C4×D12C2211yescharacteristic
38C2×C4×D12C2212yes—
39C2×C4×D12C2212yes—
40C2×#872C2212yes—
41C2×C42×D3C2211yescharacteristic
42C3×#398C2214yes—
43C3×#389C2212yes—
44C3×#389C2212yes—
45C3×#384C2212yes—
46C3×#384C2211yescharacteristic
47C3×C4×C4⋊C4C2211yescharacteristic
48C3×C4×C4⋊C4C2211yescharacteristic
49#4994C2214yes—
50#4993C2214yes—
51#4993C2214yes—
52#4991C2214yes—
53#4991C2214yes—
54#4989C2214yes—
55#4989C2214yes—
56#4988C2211yescharacteristic
57#4988C2212yes—
58#4988C2212yes—
59#4988C2212yes—
60#4988C2212yes—
61#4987C2211yescharacteristic
62#4987C2211yescharacteristic
63#4987C2211yescharacteristic
64#4987C2214yes—
65#4987C2212yes—
66#4984C2211yescharacteristic
67#4975C2211yescharacteristic
68#4975C2211yescharacteristic
69#4972C2212yes—
70#4939C2212yes—
71#4939C2212yes—
72C4×(C2×D3)⋊C4C2212yes—
73C4×C4⋊Dic3C2211yescharacteristic
74C4×Dic3⋊C4C2212yes—
75#4675C2214yes—
76#4672C2214yes—
77#4672C2214yes—
78#4671C2214yes—
79#4670C2212yes—
80#4667C2212yes—
81#4665C2212yes—
82#4665C2214yes—
83#4665C2214yes—
84#4650C2212yes—
85C2×#540—32no—
86#2856—31no—
87#2706—34no—
88#2671—34no—
89#2624—32no—
90#2552D311yescharacteristic, complemented
91#2541—31no—
92#2537—32no—
93#2501—32no—
94#2454—32no—
95#2445—32no—
96#2422—32no—
97#2416—32no—
98#2366—31no—
99D4×C4⋊C4—31no—
100C4×#121—31no—
101#2285—31no—
102C22×D12C2312yes—
103C22×D12C2312yes—
104C22×D12C2311yescharacteristic
105C22×D12C2312yes—
106C22×D12C2314yes—
107C22×D12C2314yes—
108C22×D12C2314yes—
109C22×D12C2312yes—
110C22×C4×D3C2312yes—
111C22×C4×D3C2311yescharacteristic
112C22×C4×D3C2311yescharacteristic
113C22×C4×D3C2311yescharacteristic
114C22×C4×D3C2314yes—
115C22×C4×D3C2314yes—
116C3×#125—28no—
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2314yes—
123C2×C3×C4⋊C4C2314yes—
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C42C2312yes—
128C2×C3×C42C2312yes—
129C2×C3×C42C2311yescharacteristic
130C2×(C2×D3)⋊C4C2312yes—
131C2×(C2×D3)⋊C4C2312yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2312yes—
134C2×(C2×D3)⋊C4C2312yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2312yes—
150C2×Dic3⋊C4C2312yes—
151C2×Dic3⋊C4C2312yes—
152C2×Dic3⋊C4C2312yes—
153C2×Dic3⋊C4C2312yes—
154C2×Dic3⋊C4C2314yes—
155C2×C4×Dic3C2311yescharacteristic
156C2×C4×Dic3C2311yescharacteristic
157C2×C4×Dic3C2312yes—
158C2×C4×Dic3C2311yescharacteristic
159#895—216no—
160#895—216no—
161#895—28no—
162#895—44no—
163#895—44no—
164#895—44no—
165#895—44no—
166#895D418yescomplemented
167#894—216no—
168#894—216no—
169#894—48no—
170#893—28no—
171#893—28no—
172D3×C4⋊C4—44no—
173#874—28no—
174#874—24no—
175C4×D12—24no—
176C4×D12—44no—
177C4×D12—44no—
178#872—28no—
179C42×D3—24no—
180C3×#95C2312yes—
181C3×#95C2312yes—
182C3×#95C2314yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189#540—616no—
190C2×#127—31no—
191C2×#127—32no—
192C2×#125C2×D312yes—
193C2×#123—34no—
194C2×#123—34no—
195C2×#123—34no—
196C2×#121—31no—
197C2×#121—32no—
198C2×#121—34no—
199C2×#121—34no—
200C2×#121—32no—
201C2×#121—32no—
202C2×#121—32no—
203C2×#121—32no—
204C2×C4×D4—32no—
205C2×C4×D4—32no—
206C2×C4×D4—31no—
207C2×C4×D4—32no—
208C2×C4×D4—32no—
209C2×#117—32no—
210C22×C4⋊C4—32no—
211C22×C42—31no—
212#399—34no—
213#399—34no—
214#398C2×D314yes—
215#397—34no—
216#396—34no—
217#394—34no—
218#394—34no—
219#394—34no—
220#394—34no—
221#392—34no—
222#390—32no—
223#390—32no—
224#390—32no—
225#390—32no—
226#390—31no—
227#390—32no—
228#390—32no—
229#389—32no—
230#389—31no—
231#389C2×D312yes—
232#389C2×D312yes—
233#388—32no—
234#386—34no—
235#386—32no—
236#386—34no—
237#385—34no—
238#385—34no—
239#384—31no—
240#384—31no—
241#384C2×D311yescharacteristic
242#384C2×D312yes—
243#382—32no—
244#380—32no—
245#380—31no—
246#380—31no—
247#380—34no—
248#380—31no—
249#380—32no—
250C4×C4⋊C4—31no—
251C4×C4⋊C4—32no—
252C4×C4⋊C4C2×D311yescharacteristic
253C4×C4⋊C4C2×D311yescharacteristic
254C4×C22⋊C4—32no—
255C23×D3C2414yes—
256C23×D3C2412yes—
257C23×D3C2411yescharacteristic
258C22×C3×C4C2412yes—
259C22×C3×C4C2412yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2414yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2411yescharacteristic
264C22×C3×C4C2411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C22×Dic3C2411yescharacteristic
267C22×Dic3C2412yes—
268C22×Dic3C2412yes—
269C22×Dic3C2412yes—
270C22×Dic3C2411yescharacteristic
271C22×Dic3C2411yescharacteristic
272C2×D12—22no—
273C2×D12—22no—
274C2×D12—24no—
275C2×D12—24no—
276C2×D12—24no—
277C2×D12—24no—
278C2×D12—24no—
279C2×D12—24no—
280C2×D12—28no—
281C2×D12—28no—
282C2×D12—28no—
283C2×D12—24no—
284C2×D12—42no—
285C2×D12—42no—
286C2×D12—44no—
287C2×D12—42no—
288C2×D12—44no—
289C2×D12—44no—
290C2×D12—44no—
291C2×D12—44no—
292C2×D12—42no—
293C2×D12—44no—
294C2×D12C2×D414yes—
295C2×D12C2×D418yes—
296C2×C4×D3—22no—
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3—22no—
300C2×C4×D3—24no—
301C2×C4×D3—22no—
302C2×C4×D3—24no—
303C2×C4×D3—24no—
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3—28no—
307C2×C4×D3—28no—
308C2×C4×D3—41no—
309C2×C4×D3—44no—
310C2×C4×D3—44no—
311C2×C4×D3—44no—
312C2×C4×D3—44no—
313C2×C4×D3C2×D414yes—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—28no—
316C3×C4⋊C4—28no—
317C3×C4⋊C4—24no—
318C3×C4⋊C4—22no—
319C3×C4⋊C4—22no—
320C3×C4⋊C4—22no—
321C3×C4⋊C4—44no—
322C3×C4⋊C4—42no—
323C3×C4⋊C4C2×D414yes—
324C3×C42—24no—
325C3×C42—24no—
326C3×C42#4114yes—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—28no—
330(C2×D3)⋊C4—28no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—28no—
335(C2×D3)⋊C4—44no—
336(C2×D3)⋊C4—42no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4C2×D418yes—
343C4⋊Dic3—22no—
344C4⋊Dic3—22no—
345C4⋊Dic3—22no—
346C4⋊Dic3—42no—
347Dic3⋊C4—24no—
348Dic3⋊C4—24no—
349Dic3⋊C4—24no—
350Dic3⋊C4—44no—
351Dic3⋊C4—42no—
352C4×Dic3—24no—
353C4×Dic3—22no—
354C4×Dic3—22no—
355C4×Dic3—22no—
356C22×D4—31no—
357C22×D4—32no—
358C22×D4—32no—
359C22×D4—32no—
360C22×D4—34no—
361C22×D4—34no—
362C22×D4—34no—
363C22×D4—32no—
364C23×C4—31no—
365C23×C4—32no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—34no—
369C23×C4—34no—
370#127—68no—
371#127—64no—
372#125—28no—
373#123—616no—
374#123—616no—
375#123—128no—
376#121—38no—
377#121—68no—
378#121—616no—
379#121—616no—
380#121—124no—
381#121—124no—
382#121—124no—
383#121—124no—
384C4×D4—68no—
385C4×D4—68no—
386C4×D4—64no—
387C4×D4—124no—
388C4×D4—124no—
389#117—68no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—124no—
400C2×C4⋊C4C22×D312yes—
401C2×C4⋊C4C22×D312yes—
402C2×C4⋊C4C22×D311yescharacteristic
403C2×C4⋊C4C22×D311yescharacteristic
404C2×C4⋊C4C22×D314yes—
405C2×C4⋊C4C22×D314yes—
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D312yes—
408C2×C4⋊C4C22×D314yes—
409C2×C4⋊C4C22×D311yescharacteristic
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C42—32no—
427C2×C42—31no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—64no—
431C2×C42C22×D312yes—
432C2×C42C22×D312yes—
433C2×C42C22×D311yescharacteristic
434#95—32no—
435#95—32no—
436#95—32no—
437#95—32no—
438#95—32no—
439#95—34no—
440#95C22×D312yes—
441#95C22×D312yes—
442#95C22×D314yes—
443C23×C3C2511yescharacteristic
444C22×D3—22no—
445C22×D3—21no—
446C22×D3—22no—
447C22×D3—21no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—22no—
454C22×D3—21no—
455C22×D3—22no—
456C22×D3—24no—
457C22×D3—24no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—24no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3C22×D412yes—
464C22×D3C22×D414yes—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—24no—
472C2×C3×C4—22no—
473C2×C3×C4—24no—
474C2×C3×C4—22no—
475C2×C3×C4—24no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4C22×D414yes—
482C2×C3×C4C22×D412yes—
483C2×C3×C4C2×#4112yes—
484C2×C3×C4C2×#4112yes—
485C2×C3×C4C2×#4112yes—
486C2×C3×C4H(5,𝔽2)12yes—
487C2×C3×C4H(5,𝔽2)12yes—
488C2×C3×C42−1+412yes—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—21no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—21no—
502C2×Dic3—22no—
503C2×Dic3—21no—
504C2×Dic3—22no—
505C2×Dic3C22×D412yes—
506C2×Dic3H(5,𝔽2)12yes—
507D12—28no—
508D12—48no—
509D12—48no—
510D12—48no—
511D12—84no—
512D12—88no—
513D12—88no—
514D12—88no—
515C4×D3—28no—
516C4×D3—44no—
517C4×D3—44no—
518C4×D3—48no—
519C4×D3—88no—
520C4×D3—88no—
521C24—32no—
522C24—31no—
523C24—34no—
524C2×D4—34no—
525C2×D4—38no—
526C2×D4—68no—
527C2×D4—68no—
528C2×D4—68no—
529C2×D4—64no—
530C2×D4—62no—
531C2×D4—64no—
532C2×D4—64no—
533C2×D4—64no—
534C2×D4—62no—
535C2×D4—64no—
536C2×D4—64no—
537C2×D4—64no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—124no—
542C2×D4—124no—
543C2×D4—124no—
544C2×D4—124no—
545C2×D4—124no—
546C2×D4—122no—
547C2×D4—124no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—34no—
551C22×C4—31no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—62no—
556C22×C4—68no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—64no—
562C22×C4—64no—
563C22×C4—62no—
564C22×C4—64no—
565C22×C4—62no—
566C22×C4—68no—
567C22×C4—121no—
568C22×C4—124no—
569C22×C4—124no—
570C22×C4—124no—
571C22×C4—124no—
572C22×C4C23×D312yes—
573C22×C4C23×D312yes—
574C22×C4C23×D312yes—
575C22×C4C23×D314yes—
576C22×C4C23×D312yes—
577C22×C4C23×D311yescharacteristic
578C22×C4C23×D311yescharacteristic
579C22×C4C23×D311yescharacteristic
580C4⋊C4—24no—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—22no—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4—64no—
590C4⋊C4—64no—
591C4⋊C4—64no—
592C4⋊C4—62no—
593C4⋊C4—62no—
594C4⋊C4—62no—
595C4⋊C4—124no—
596C4⋊C4—122no—
597C4⋊C4—122no—
598C4⋊C4D3×D414yes—
599C22⋊C4—38no—
600C22⋊C4—68no—
601C22⋊C4—68no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C22⋊C4—64no—
605C22⋊C4—68no—
606C22⋊C4—68no—
607C22⋊C4—64no—
608C22⋊C4—122no—
609C22⋊C4—124no—
610C22⋊C4—122no—
611C22⋊C4—124no—
612C22⋊C4—124no—
613C22⋊C4—124no—
614C22⋊C4—124no—
615C42—24no—
616C42—24no—
617C42—64no—
618C42—62no—
619C42—62no—
620C42—62no—
621C42#23914yes—
622C22×C3C23×D411yescharacteristic
623C22×C3C22×#4111yescharacteristic
624C22×C3C2×H(5,𝔽2)11yescharacteristic
625C22×C3C2×H(5,𝔽2)11yescharacteristic
626C22×C3C2×H(5,𝔽2)11yescharacteristic
627C22×C3C2×2−1+411yescharacteristic
628C22×C3#58511yescharacteristic
629C2×D3—22no—
630C2×D3—24no—
631C2×D3—22no—
632C2×D3—24no—
633C2×D3—24no—
634C2×D3—22no—
635C2×D3—42no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—41no—
641C2×D3—42no—
642C2×D3—41no—
643C2×D3—44no—
644C2×D3—44no—
645C2×D3—44no—
646C2×D3—44no—
647C2×D3—44no—
648C2×D3—44no—
649C2×D3—44no—
650C3×C4—22no—
651C3×C4—24no—
652C3×C4—42no—
653C3×C4—44no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4#54014yescomplemented
657C3×C4#54714yes—
658Dic3—22no—
659Dic3—22no—
660Dic3—41no—
661Dic3—42no—
662Dic3—42no—
663Dic3—42no—
664C23—34no—
665C23—32no—
666C23—62no—
667C23—61no—
668C23—61no—
669C23—62no—
670C23—61no—
671C23—62no—
672C23—62no—
673C23—61no—
674C23—62no—
675C23—61no—
676C23—61no—
677C23—62no—
678C23—64no—
679C23—64no—
680C23—64no—
681C23—64no—
682C23—64no—
683C23—64no—
684C23—64no—
685C23C24×D311yescharacteristic
686D4—68no—
687D4—128no—
688D4—128no—
689D4—128no—
690D4—244no—
691D4—248no—
692D4—248no—
693D4—248no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—68no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—61no—
720C2×C4—62no—
721C2×C4—61no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—61no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—124no—
730C2×C4—124no—
731C2×C4—128no—
732C2×C4—248no—
733C2×C4—248no—
734C2×C4C2×D3×D414yes—
735C2×C4C2×D3×D412yes—
736C2×C4C2×#23912yes—
737C2×C4C2×#23912yes—
738C2×C4C2×#23912yes—
739C2×C4#100712yes—
740C2×C4#100912yes—
741C2×C4#100912yes—
742C2×C3C2×#54011yescharacteristic
743C2×C3C2×#54711yescharacteristic
744C2×C3#349411yescharacteristic
745C2×C3#349611yescharacteristic
746C2×C3#349811yescharacteristic
747C2×C3#354811yescharacteristic
748C2×C3#355411yescharacteristic
749D3—42no—
750D3—44no—
751D3—84no—
752C22—62no—
753C22—64no—
754C22—62no—
755C22—64no—
756C22—64no—
757C22—62no—
758C22—121no—
759C22—122no—
760C22—122no—
761C22—121no—
762C22—121no—
763C22—122no—
764C22—121no—
765C22—122no—
766C22—124no—
767C22—124no—
768C22—124no—
769C22—124no—
770C22—124no—
771C22—124no—
772C22—124no—
773C22C22×D3×D411yescharacteristic
774C22C22×#23911yescharacteristic
775C22C2×#100711yescharacteristic
776C22C2×#100911yescharacteristic
777C22C2×#100911yescharacteristic
778C22D3×H(5,𝔽2)11yescharacteristic
779C22#596811yescharacteristic
780C4—22no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—44no—
785C4—42no—
786C4—62no—
787C4—62no—
788C4—121no—
789C4—122no—
790C4—122no—
791C4—122no—
792C4#569714yescomplemented
793C4#572614yes—
794C3#3935211yescharacteristic, complemented, Sylow
795C2—122no—
796C2—124no—
797C2—244no—
798C2C2×#569711yescharacteristic
799C2C2×#572611yescharacteristic
800C2#8659711yescharacteristic
801C2#8670211yescharacteristic
802C2#8677011yescharacteristic
803C2#8693911yescharacteristic
804C2#8703511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2552C2
hypercenter#2552D3
hypocenterC3#39352
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2552

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#5697C2semidirect
2. C3×#2552C2semidirect
3. #83030C2semidirect
4. #77967C2semidirect
5. #77853C2semidirect
6. #76249C2semidirect
7. #76215C2semidirect
8. #76211C2semidirect
9. #76004C2semidirect
10. #74375C2semidirect
11. #74368C2semidirect
12. #74360C2semidirect
13. #74328C2semidirect
14. #73799C2semidirect
15. C4×#895C2semidirect
16. #73753C2semidirect
17. #73653C2semidirect
90. #2552D3semidirect
166. #895D4semidirect
656. C3×C4#540semidirect
792. C4#5697semidirect
794. C3#39352semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#56972
C3×#25522
#830302
#779672
#778532
#762492
#762152
#762112
#760042
#743752
#743682
#743602
#743282
#737992
C4×#8952
#737532
#736532
#393523